Phasors vs Vectors:

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rattus

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Just struck me! The math is different for phasors and vectors, e.g.,

Draw three 120 unit arrows in a wye, 120 degrees apart.

If they are force vectors:

To obtain the effect of any two vectors we simply add them with trig, that is,

F1 + F2 = 120 lbs x 2cos(60) = 120 lbs x 1 = 120 lbs.

If they are voltage phasors:

To obtain the voltage between we must subtract the two phasors with trig, that is,

Va - Vb = 120V x 2cos(30) = 120V x 1.732 = 208V

Both results are correct.

Try it!
 
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rattus said:
Try it!
Click to expand...
Uhh ... I think I'll just take your word for it.
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rattus said:
Just struck me! The math is different for phasors and vectors, e.g.,

Draw three 120 unit arrows in a wye, 120 degrees apart.

If they are force vectors:

To obtain the effect of any two vectors we simply add them with trig, that is,

F1 + F2 = 120 x 2cos(60) = 120

If they are voltage phasors:

To obtain the voltage between we must subtract the two phasors with trig, that is,

Va - Vb = 120V x 2cos(60) = 120 x 1.732

Both results are correct.

Try it!
Click to expand...

Exactly where did it strike you and was it possibly too hard:smile:

Check your math. Looks a little strange to me that the same product of " 120 x 2cos(60)" gives two different results?
Its too early for me to do trig but ...

If they were force vectors the "addition" would result in a very small net force magnitude. Think about two people pulling on a rope at 180 degrees from each other. The net force is zero. Now have them rotate to 120 degrees. Now there is a net force greater than zero but not equal to 120.
Forget the confusing math and do it on graph paper.

When they are voltage you are looking for a potential "difference" so you then get the 208 result. One vector is reversed in direction and then added to the other. The two produce totally different results.

One is addition and one is subtraction. Thus totally different results...
 
Oops!

Oops!

ELA said:
Exactly where did it strike you and was it possibly too hard:smile:

Check your math. Looks a little strange to me that the same product of " 120 x 2cos(60)" gives two different results?
Its too early for me to do trig but ...

If they were force vectors the "addition" would result in a very small net force magnitude. Think about two people pulling on a rope at 180 degrees from each other. The net force is zero. Now have them rotate to 120 degrees. Now there is a net force greater than zero but not equal to 120.
Forget the confusing math and do it on graph paper.

When they are voltage you are looking for a potential "difference" so you then get the 208 result. One vector is reversed in direction and then added to the other. The two produce totally different results.

One is addition and one is subtraction. Thus totally different results...
Click to expand...

Typed in the wrong angle! You are the first to notice.

Yes, 120 lbs is correct. Two ropes pulling 120 lbs each at 120 degrees apart each contribute 60 lbs--cos(60).

Of course 208V is also correct.
 
rattus said:
Draw three 120 unit arrows in a wye, 120 degrees apart.

If they are force vectors:

To obtain the effect of any two vectors we simply add them with trig, that is,

F1 + F2 = 120 x 2cos(60) = 120 x 1

If they are voltage phasors:

To obtain the voltage between we must subtract the two phasors with trig, that is,

Va - Vb = 120V x 2cos(60) = 120 x 1.732
Click to expand...

TI-84 Plus Calc gives
F1 + F2 = 120V * 2cos(60) = 120 * -1.90 or -228.58
Va - Vb = 120V * 2cos(60) = 120 * -1.90 or -228.58
You are saying F1 + F2 equals -228.58
You are also saying Va + Vb equals -228.58

You are missing some steps in your math to get here.Refer to American Electricians Handbook 14th edition pages 1.62
 
I get the same result

120V * 2Cos(60)= 120V *-1.904 = -228.57

Why are you using the term 2Cos(60)? I see that when you put the two 120V vectors head to tail the angle that is formed will be 60 degrees, but I dont understand where the 2 is coming fromin the 2Cos(60) or how you are getting your results
 
mull982 said:
I get the same result

120V * 2Cos(60)= 120V *-1.904 = -228.57

Why are you using the term 2Cos(60)? I see that when you put the two 120V vectors head to tail the angle that is formed will be 60 degrees, but I dont understand where the 2 is coming fromin the 2Cos(60) or how you are getting your results
Click to expand...

I think you have the calculator set on Radians instead of Degrees.
cos(60deg) = .5

cos(60rad) = -.95

:smile:
 
If you are using excel for your calculations, try this:

=cos(radians(60))

excel assumes you are entering radians. So, if you want to use degrees, you have to convert them to radians first.
 
Using degrees on the TI-84 gets .5

On Ti-83s and up if in radians you can type cos(DEGx) to convert and also cos(RADx) to go back

No editing of the original post after answers and questions have been posted.

on Va - Vb the 2cos(60) is now 2cos(30)
Naughty.

Now 120 * 2cos(30) is 207.85
 
Yes my calculator was in radians, and I now am able to get the correct answer using degrees. Thank You

Can someone explain why we use 2Cos(30) for this calculation? I sort of see why we use it but dont quite completely understand. Can someone shed some light?
 
rattus said:
Just struck me! The math is different for phasors and vectors, e.g.,

Draw three 120 unit arrows in a wye, 120 degrees apart.

If they are force vectors:

To obtain the effect of any two vectors we simply add them with trig, that is,

F1 + F2 = 120 lbs x 2cos(60) = 120 lbs x 1 = 120 lbs.

If they are voltage phasors:

To obtain the voltage between we must subtract the two phasors with trig, that is,

Va - Vb = 120V x 2cos(30) = 120V x 1.732 = 208V

Both results are correct.

Try it!
Click to expand...

Thanks for pointing out the obvious. :)
 
Go back to the original post please:

Go back to the original post please:

I have edited the original post to correct a careless error.

Everything else is in order.

Now we can see that vectors and phasors are not the same animals.
 
Substraction!

Substraction!

mull982 said:
Yes my calculator was in radians, and I now am able to get the correct answer using degrees. Thank You

Can someone explain why we use 2Cos(30) for this calculation? I sort of see why we use it but dont quite completely understand. Can someone shed some light?
Click to expand...

If you do the subtraction graphically, you reverse one of the arrows. This causes the resultant phasors to be 60 degrees apart instead of 120.
 
Typo!

Typo!

mull982 said:
I get the same result

120V * 2Cos(60)= 120V *-1.904 = -228.57

Why are you using the term 2Cos(60)? I see that when you put the two 120V vectors head to tail the angle that is formed will be 60 degrees, but I dont understand where the 2 is coming fromin the 2Cos(60) or how you are getting your results
Click to expand...

Should be 2cos(30) which is 1.732. Typo in original post. '

After reversing one of the arrows, it is obvious that each phasor contributes 1/2 to the result. Guess I will have to draw a diagram and check it thrice.
 
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On a TI-85:
(120/0) - (120/-120) = (x,y)
Ans >Pol = (207.846/30)

(120/0) + (120/-120) = (x,y)
Ans >Pol = (120/-60)
 
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Backwards:

Backwards:

Mr. Bill said:
On a TI-85:
(120/0) + (120/-120) = (x,y)
Ans >Pol = (207.846/30)

(120/0) - (120/-120) = (x,y)
Ans >Pol = (120/-60)
Click to expand...

The sum of the vectors is 120.

The difference of the phasors is 208.
 
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